Discrete topology optimization in augmented space: integrated element removal for minimum size and mesh sensitivity cont
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RESEARCH PAPER
Discrete topology optimization in augmented space: integrated element removal for minimum size and mesh sensitivity control Alireza Asadpoure1
· Mojtaba Harati2 · Mazdak Tootkaboni1
Received: 19 July 2019 / Revised: 1 May 2020 / Accepted: 10 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A computational strategy is proposed to circumvent some of the major issues that arise in the classical threshold-based approach to discrete topology optimization. These include the lack of an integrated element removal strategy to prevent the emergence of hair-like elements, the inability to effectively enforce a minimum member size of arbitrary magnitude, and high sensitivity of the final solution to the choice of ground structure. The proposed strategy draws upon the ideas used to arrive at mesh-independent solutions in continuum topology optimization and enables efficient imposition of a minimum size constraint onto the set of non vanishing elements. This is achieved via augmenting the design variables by a set of auxiliary variables, called existence variables, that not only prove very effective in addressing the aforementioned issues but also bring in a set of added benefits such as better convergence and complexity control. 2D and 3D examples from trusslike structures are presented to demonstrate the superiority of the proposed approach over the classical approach to discrete topology optimization. Keywords Topology optimization · Discrete design · Mesh sensitivity · Minimum size constraint · Hair-like elements · Complexity control
1 Introduction Among different optimization paradigms, topology optimization has recently gained significant attention due to its ability to extend the design space to incorporate shape, size and topological changes simultaneously (Sigmund and Maute 2013; Deaton and Grandhi 2014). In a discrete setting (e.g. truss, frame, lattice structures) the process of finding the optimized layout of the material through topology optimization is often formulated using the Ground Structure Method (GSM) (Dorn et al. 1964) which starts from an initial guess or ground structure (GS); normally a very dense mesh of interconnected (and possibly overlapping) bar elements. In the “classical” approach to GSM, a gradient-based computational optimizer marches towards
Responsible Editor: James K Guest Alireza Asadpoure
[email protected] 1
Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, MA 02747, USA
2
Department of Civil Engineering, University of Science and Culture, Rasht, Guilan, Iran
the solution through element re-sizing (informed by the sensitives of the objective and constraints) and an element removal strategy where from the multitude of members within the ground structure, those with vanishing cross sections are gradually removed from the design domain. The size of design space in GSM, defined by the density and complexity (e.g. level of connectivity) of initial mesh, is often decided at the onset of optimiza
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